Systems and methods for production of low oxygen content silicon

ABSTRACT

A method for producing a silicon ingot includes withdrawing a seed crystal from a melt that includes melted silicon in a crucible that is enclosed in a vacuum chamber containing a cusped magnetic field. At least one process parameter is regulated in at least two stages, including a first stage corresponding to formation of the silicon ingot up to an intermediate ingot length, and a second stage corresponding to formation of the silicon ingot from the intermediate ingot length to the total ingot length. During the second stage process parameter regulation may include reducing a crystal rotation rate, reducing a crucible rotation rate, and/or increasing a magnetic field strength relative to the first stage.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Patent Application Ser. No.62/263,355, filed 4 Dec. 2015, which is hereby incorporated by referencein its entirety.

FIELD

This disclosure generally relates to the production of silicon ingots,and more specifically, to methods and systems for producing siliconingots having a low oxygen concentration.

BACKGROUND

Single crystal silicon is the starting material in many processes forfabricating semiconductor electronic components and solar materials. Forexample, semiconductor wafers produced from silicon ingots are commonlyused in the production of integrated circuit chips. In the solarindustry, single crystal silicon may be used instead of multicrystallinesilicon due to the absence of grain boundaries and dislocations. Singlecrystal silicon ingots are machined into a desired shape, such as asilicon wafer, from which the semiconductor or solar wafers can beproduced

Existing methods to produce high-purity single crystal silicon ingotinclude a float zone method and a magnetic field applied Czochralski(MCZ) process. The float zone method includes melting a narrow region ofa rod of ultrapure polycrystalline silicon and slowly translating themolten region along the rod to produce a single crystal silicon ingot ofhigh purity. The MCZ process produces single crystal silicon ingots bymelting polycrystalline silicon in a crucible, dipping a seed crystalinto the molten silicon, and withdrawing the seed crystal in a mannersufficient to achieve the diameter desired for the ingot. A horizontaland/or vertical magnetic field may be applied to the molten silicon toinhibit the incorporation of impurities, such as oxygen, into thegrowing single crystal silicon ingot. Although float zone silicon ingotstypically contain relatively low concentrations of impurities, such asoxygen, the diameter of ingots grown using the float zone method aretypically no larger than about 150 mm due to limitations imposed bysurface tension. MCZ silicon ingots may be produced at higher ingotdiameters compared to float zone ingots, but MCZ silicon ingotstypically contain higher concentrations of impurities.

During the process of producing single crystal silicon ingots using theMCZ method, oxygen is introduced into silicon crystal ingots through amelt-solid or melt crystal interface. The oxygen may cause variousdefects in wafers produced from the ingots, reducing the yield ofsemiconductor devices fabricated using the ingots. For example,insulated-gate bipolar transistors (IGBTs), high quality radio-frequency(RF), high resistivity silicon on insulator (HR-SOI), and charge traplayer SOI (CTL-SOI) applications typically require a low oxygenconcentration (Oi) in order to achieve high resistivity.

At least some known semiconductor devices are fabricated using floatzone silicon materials to achieve a low Oi and high resistivity.However, float zone materials are relatively expensive and are limitedto use in producing ingots having a diameter less than approximately 200mm. Accordingly, float zone silicon materials are expensive and unableto produce higher diameter silicon crystal ingots with a relatively lowoxygen concentration.

This Background section is intended to introduce the reader to variousaspects of art that may be related to various aspects of the presentdisclosure, which are described and/or claimed below. This discussion isbelieved to be helpful in providing the reader with backgroundinformation to facilitate a better understanding of the various aspectsof the present disclosure. Accordingly, it should be understood thatthese statements are to be read in this light, and not as admissions ofprior art.

BRIEF SUMMARY

In one aspect, a method for producing a silicon ingot includeswithdrawing a seed crystal from a melt that includes melted silicon in acrucible. The crucible is enclosed in a vacuum chamber containing acusped magnetic field. The method further includes regulating at leastone process parameter in at least two stages. The at least one processparameter includes one of a crystal rotation rate, a crucible rotationrate, and a magnetic field strength. The at least two stages include afirst stage corresponding to formation of the silicon ingot up to anintermediate ingot length, and a second stage corresponding to formationof the silicon ingot from the intermediate ingot length to the totalingot length. According to the method in this embodiment, regulating theat least one process parameter during the second stage includes at leastone of reducing the crystal rotation rate relative to the crystalrotation rate during the first stage, reducing the crucible rotationrate relative to the crucible rotation rate during the first stage, andincreasing magnetic field strength relative to magnetic field strengthduring the first stage.

Another aspect is directed to a wafer generated from a silicon ingotproduced using the method described above.

Still another aspect is directed to a crystal growing system forproducing a silicon ingot. The system comprises a vacuum chamber and acrucible disposed within the vacuum chamber. The crucible is rotatableabout an axis of symmetry, and is configured to hold a melt includingmolten silicon. A pull shaft is movable along the axis of symmetry, isrotatable about the axis of symmetry, and is configured to hold a seedcrystal. At least one magnet can generate a controllable cusped magneticfield within the crucible. A control unit comprises a processor and amemory, the memory storing instruction that, when executed by theprocessor, causes the processor to withdraw the seed crystal from a meltin the crucible to form the silicon ingot. The unit also regulates atleast one process parameter, wherein the at least one process parameteris regulated in at least two stages. The at least two stages comprise afirst stage corresponding to formation of the silicon ingot up to anintermediate ingot length, and a second stage corresponding to formationof the silicon ingot from the intermediate ingot length to the totalingot length. The instruction, when executed by the processor, causesthe processor to regulate the at least one process parameter by at leastone of reducing a crystal rotation rate relative to the crystal rotationrate during the first stage, reducing a crucible rotation rate relativeto the crucible rotation rate during the first stage, and increasing amagnetic field strength produced by the at least one magnet relative tothe magnetic field strength produced by the at least one magnet duringthe first stage.

Various refinements exist of the features noted in relation to theabove-mentioned aspect. Further features may also be incorporated in theabove-mentioned aspect as well. These refinements and additionalfeatures may exist individually or in any combination. For instance,various features discussed below in relation to any of the illustratedembodiments may be incorporated into the above-described aspect, aloneor in any combination.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view of a crucible of one embodiment.

FIG. 2 is a side view of the crucible shown in FIG. 1.

FIG. 3 is a schematic illustrating a cusped magnetic field applied to acrucible containing a melt in a crystal growing apparatus.

FIG. 4 is a block diagram of a crystal growing system of same embodimentas FIG. 1.

FIG. 5A is a cross-sectional view of a portion of a crucible showingflowlines and oxygen concentration near the crucible wall atintermediate body growth at a given crystal rotation rate.

FIG. 5B is a cross-sectional view of a portion of an example cruciblemapping flowlines and oxygen concentration near the crucible wall atlate body growth at a crystal rotation rate.

FIG. 5C is a cross-sectional view of a portion of a crucible mappingflowlines and oxygen concentration near the crucible wall at late bodygrowth at a different crystal rotation rate.

FIG. 6 is a graph plotting a simulated oxygen concentration (0 i) as afunction of crystal rotation rate at late body growth versus position(BL) along the crystal.

FIG. 7A is a graph plotting an oxygen concentration at late body growthversus crucible rotation rate for a crystal body rotation rate of 6 rpm.

FIG. 7B is a graph plotting an oxygen concentration at late body growthversus crucible rotation rate for a crystal body rotation rate of 8 rpm.

FIG. 8A is a cross-sectional view of an example crucible mappingflowlines and velocity magnitudes near a crucible wall at late bodygrowth at a magnetic field strength corresponding to 50% balanced.

FIG. 8B is a cross-sectional view of an example crucible mappingflowlines and velocity magnitudes near a crucible wall at late bodygrowth at a magnetic field strength corresponding to 95% balanced.

FIG. 8C is a cross-sectional view of an example crucible mappingflowlines and velocity magnitudes near a crucible wall at late bodygrowth at a magnetic field strength corresponding to 150% balanced.

FIG. 9 is a graph plotting oxygen concentration as a function of crystalbody length for two different crystal rotation rate profiles.

FIG. 10 is a block diagram of an example server system.

FIG. 11 is a block diagram of an example computing device.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Referring initially to FIGS. 1 and 2, a crucible of one embodiment isindicated generally at 10. A cylindrical coordinate system for crucible10 includes a radial direction R 12, an angular direction θ 14, and anaxial direction Z 16. Coordinates R 12, θ 14, and Z 16 are used hereinto describe methods and systems for producing low oxygen silicon ingots.The crucible 10 contains a melt 25 having a melt surface 36. A crystal27 is grown from the melt 25. The melt 25 may contain one or moreconvective flow cells 17, 18 induced by heating of the crucible 10 androtation of the crucible 10 and/or crystal 27 in the angular direction θ14. The structure and interaction of these one or more convective flowcells 17, 18 are modulated via regulation of one of more processparameters to reduce the inclusion of oxygen within the forming crystal27 as described in detail herein below.

FIG. 3 is a block diagram illustrating a cusped magnetic field beingapplied to crucible 10 containing melt 25 in a crystal growingapparatus. As shown, crucible 10 contains silicon melt 25 from which acrystal 27 is grown. The cusped magnetic field configuration is designedto overcome deficiencies of axial and horizontal magnetic fieldconfigurations. A pair of coils 31 and 33 (e.g., Helmholtz coils) areplaced coaxially above and below melt surface 36. Coils 31 and 33 areoperated in an opposed current mode to generate a magnetic field thathas a purely radial field component (i.e., along R 12) near melt surface36 and a purely axial field component (i.e., along Z 16) near an axis ofsymmetry 38 of crystal 27. The combination of an upper magnetic field 40and a lower magnetic field 42 produced by coils 31 and 33, respectively,results in axial and radial cusped magnetic field components.

FIG. 4 is a block diagram of a crystal growing system 100. The crystalgrowing system 100, elements of the crystal growing system 100, andvarious operating parameters of the crystal growing system 100 aredescribed in additional detail in PCT Published Application 2014/190165,which is incorporated by reference herein in its entirety. Referringagain to FIG. 4, system 100 employs a Czochralski crystal growth methodto produce a semiconductor ingot. In this embodiment, system 100 isconfigured to produce a cylindrical semiconductor ingot having an ingotdiameter of greater than one-hundred fifty millimeters (150 mm), morespecifically in a range from approximately 150 mm to 460 mm, and evenmore specifically, a diameter of approximately three-hundred millimeters(300 mm). In other embodiments, system 100 is configured to produce asemiconductor ingot having a two-hundred millimeter (200 mm) ingotdiameter or a four-hundred and fifty millimeter (450 mm) ingot diameter.In addition, in one embodiment, system 100 is configured to produce asemiconductor ingot with a total ingot length of at least nine hundredmillimeters (900 mm). In other embodiments, system 100 is configured toproduce a semiconductor ingot with a total ingot length ranging fromapproximately nine hundred millimeters (900 mm) to twelve hundredmillimeters (1200 mm).

Referring again to FIG. 4, the crystal growing system 100 includes avacuum chamber 101 enclosing crucible 10. A side heater 105, forexample, a resistance heater, surrounds crucible 10. A bottom heater106, for example, a resistance heater, is positioned below crucible 10.During heating and crystal pulling, a crucible drive unit 107 (e.g., amotor) rotates crucible 10, for example, in the clockwise direction asindicated by the arrow 108. Crucible drive unit 107 may also raiseand/or lower crucible 10 as desired during the growth process. Withincrucible 10 is silicon melt 25 having a melt level or melt surface 36.In operation, system 100 pulls a single crystal 27, starting with a seedcrystal 115 attached to a pull shaft or cable 117, from melt 25. One endof pull shaft or cable 117 is connected by way of a pulley (not shown)to a drum (not shown), or any other suitable type of lifting mechanism,for example, a shaft, and the other end is connected to a chuck (notshown) that holds seed crystal 115 and crystal 27 grown from seedcrystal 115.

Crucible 10 and single crystal 27 have a common axis of symmetry 38.Crucible drive unit 107 can raise crucible 10 along axis 38 as the melt25 is depleted to maintain melt level 36 at a desired height. A crystaldrive unit 121 similarly rotates pull shaft or cable 117 in a direction110 opposite the direction in which crucible drive unit 107 rotatescrucible 10 (e.g., counter-rotation). In embodiments using iso-rotation,crystal drive unit 121 may rotate pull shaft or cable 117 in the samedirection in which crucible drive unit 107 rotates crucible 10 (e.g., inthe clockwise direction). Iso-rotation may also be referred to as aco-rotation. In addition, crystal drive unit 121 raises and lowerscrystal 27 relative to melt level 36 as desired during the growthprocess.

According to the Czochralski single crystal growth process, a quantityof polycrystalline silicon, or polysilicon, is charged to crucible 10. Aheater power supply 123 energizes resistance heaters 105 and 106, andinsulation 125 lines the inner wall of vacuum chamber 101. A gas supply127 (e.g., a bottle) feeds argon gas to vacuum chamber 101 via a gasflow controller 129 as a vacuum pump 131 removes gas from vacuum chamber101. An outer chamber 133, which is fed with cooling water from areservoir 135, surrounds vacuum chamber 101.

The cooling water is then drained to a cooling water return manifold137. Typically, a temperature sensor such as a photocell 139 (orpyrometer) measures the temperature of melt 25 at its surface, and adiameter transducer 141 measures a diameter of single crystal 27. Inthis embodiment, system 100 does not include an upper heater. Thepresence of an upper heater, or lack of an upper heater, alters coolingcharacteristics of crystal 27.

An upper magnet, such as solenoid coil 31, and a lower magnet, such assolenoid coil 33, are located above and below, respectively, melt level36 in this embodiment. The coils 31 and 33, shown in cross-section,surround vacuum chamber (not shown) and share axes with axis of symmetry38. In one embodiment, the upper and lower coils 31 and 33 have separatepower supplies, including, but not limited to, an upper coil powersupply 149 and a lower coil power supply 151, each of which is connectedto and controlled by control unit 143.

In this embodiment, current flows in opposite directions in the twosolenoid coils 31 and 33 to produce a magnetic field (as shown in FIG.3). A reservoir 153 provides cooling water to the upper and lower coils31 and 33 before draining via cooling water return manifold 137. Aferrous shield 155 surrounds coils 31 and 33 to reduce stray magneticfields and to enhance the strength of the field produced.

A control unit 143 is used to regulate the plurality of processparameters including, but not limited to, at least one of crystalrotation rate, crucible rotation rate, and magnetic field strength. Invarious embodiments, the control unit 143 may include a processor 144that processes the signals received from various sensors of the system100 including, but not limited to, photocell 139 and diameter transducer141, as well as to control one or more devices of system 100 including,but not limited to: crucible drive unit 107, crystal drive unit 121,heater power supply 123, vacuum pump 131, gas flow controller 129 (e.g.,an argon flow controller), upper coil power supply 149, lower coil powersupply 151, and any combination thereof.

Control unit 143 may be a computer system. Computer systems, asdescribed herein, refer to any known computing device and computersystem. As described herein, all such computer systems include aprocessor and a memory. However, any processor in a computer systemreferred to herein may also refer to one or more processors wherein theprocessor may be in one computing device or a plurality of computingdevices acting in parallel. Additionally, any memory in a computerdevice referred to herein may also refer to one or more memories whereinthe memories may be in one computing device or a plurality of computingdevices acting in parallel.

The term processor, as used herein, refers to central processing units,microprocessors, microcontrollers, reduced instruction set circuits(RISC), application specific integrated circuits (ASIC), logic circuits,and any other circuit or processor capable of executing the functionsdescribed herein. The above are examples only, and are thus not intendedto limit in any way the definition and/or meaning of the term“processor.”

As used herein, the term “database” may refer to either a body of data,a relational database management system (RDBMS), or to both. As usedherein, a database may include any collection of data includinghierarchical databases, relational databases, flat file databases,object-relational databases, object oriented databases, and any otherstructured collection of records or data that is stored in a computersystem. The above examples are example only, and thus are not intendedto limit in any way the definition and/or meaning of the term database.Examples of RDBMS's include, but are not limited to including, Oracle®Database, MySQL, IBM® DB2, Microsoft® SQL Server, Sybase®, andPostgreSQL. However, any database may be used that enables the systemsand methods described herein. (Oracle is a registered trademark ofOracle Corporation, Redwood Shores, Calif.; IBM is a registeredtrademark of International Business Machines Corporation, Armonk, N.Y.;Microsoft is a registered trademark of Microsoft Corporation, Redmond,Wash.; and Sybase is a registered trademark of Sybase, Dublin, Calif.)

In one embodiment, a computer program is provided to enable control unit143, and this program is embodied on a computer readable medium. In anexample embodiment, the computer system is executed on a single computersystem, without requiring a connection to a server computer. In afurther embodiment, the computer system is run in a Windows® environment(Windows is a registered trademark of Microsoft Corporation, Redmond,Wash.). In yet another embodiment, the computer system is run on amainframe environment and a UNIX® server environment (UNIX is aregistered trademark of X/Open Company Limited located in Reading,Berkshire, United Kingdom). Alternatively, the computer system is run inany suitable operating system environment. The computer program isflexible and designed to run in various different environments withoutcompromising any major functionality. In some embodiments, the computersystem includes multiple components distributed among a plurality ofcomputing devices. One or more components may be in the form ofcomputer-executable instructions embodied in a computer-readable medium.

The computer systems and processes are not limited to the specificembodiments described herein. In addition, components of each computersystem and each process can be practiced independent and separate fromother components and processes described herein. Each component andprocess also can be used in combination with other assembly packages andprocesses.

In one embodiment, the computer system may be configured as a serversystem. FIG. 10 illustrates an example configuration of a server system301 used to receive measurements from one or more sensors including, butnot limited to: temperature sensor 139, diameter transducer 141, and anycombination thereof, as well as to control one or more devices of system100 including, but not limited to: crucible drive unit 107, crystaldrive unit 121, heater power supply 123, vacuum pump 131, gas flowcontroller 129 (e.g., an argon flow controller), upper coil power supply149, lower coil power supply 151, and any combination thereof asdescribed herein and illustrated in FIG. 4 in one embodiment. Referringagain to FIG. 10, server system 301 may also include, but is not limitedto, a database server. In this example embodiment, server system 301performs all of the steps used to control one or more devices of system100 as described herein.

Server system 301 includes a processor 305 for executing instructions.Instructions may be stored in a memory area 310, for example. Processor305 may include one or more processing units (e.g., in a multi-coreconfiguration) for executing instructions. The instructions may beexecuted within a variety of different operating systems on the serversystem 301, such as UNIX, LINUX, Microsoft Windows®, etc. It should alsobe appreciated that upon initiation of a computer-based method, variousinstructions may be executed during initialization. Some operations maybe required in order to perform one or more processes described herein,while other operations may be more general and/or specific to aparticular programming language (e.g., C, C#, C++, Java, or any othersuitable programming languages).

Processor 305 is operatively coupled to a communication interface 315such that server system 301 is capable of communicating with a remotedevice such as a user system or another server system 301. For example,communication interface 315 may receive requests (e.g., requests toprovide an interactive user interface to receive sensor inputs and tocontrol one or more devices of system 100 from a client system via theInternet.

Processor 305 may also be operatively coupled to a storage device 134.Storage device 134 is any computer-operated hardware suitable forstoring and/or retrieving data. In some embodiments, storage device 134is integrated in server system 301. For example, server system 301 mayinclude one or more hard disk drives as storage device 134. In otherembodiments, storage device 134 is external to server system 301 and maybe accessed by a plurality of server systems 301. For example, storagedevice 134 may include multiple storage units such as hard disks orsolid state disks in a redundant array of inexpensive disks (RAID)configuration. Storage device 134 may include a storage area network(SAN) and/or a network attached storage (NAS) system.

In some embodiments, processor 305 is operatively coupled to storagedevice 134 via a storage interface 320. Storage interface 320 is anycomponent capable of providing processor 305 with access to storagedevice 134. Storage interface 320 may include, for example, an AdvancedTechnology Attachment (ATA) adapter, a Serial ATA (SATA) adapter, aSmall Computer System Interface (SCSI) adapter, a RAID controller, a SANadapter, a network adapter, and/or any component providing processor 305with access to storage device 134.

Memory area 310 may include, but is not limited to, random access memory(RAM) such as dynamic RAM (DRAM) or static RAM (SRAM), read-only memory(ROM), erasable programmable read-only memory (EPROM), electricallyerasable programmable read-only memory (EEPROM), and non-volatile RAM(NVRAM). The above memory types are exemplary only, and are thus notlimiting as to the types of memory usable for storage of a computerprogram.

In another embodiment, the computer system may be provided in the formof a computing device, such as a computing device 402 (shown in FIG.11). Computing device 402 includes a processor 404 for executinginstructions. In some embodiments, executable instructions are stored ina memory area 406. Processor 404 may include one or more processingunits (e.g., in a multi-core configuration). Memory area 406 is anydevice allowing information such as executable instructions and/or otherdata to be stored and retrieved. Memory area 406 may include one or morecomputer-readable media.

In another embodiment, the memory included in the computing device ofthe control unit 143 may include a plurality of modules. Each module mayinclude instructions configured to execute using at least one processor.The instructions contained in the plurality of modules may implement atleast part of the method for simultaneously regulating a plurality ofprocess parameters as described herein when executed by the one or moreprocessors of the computing device. Non-limiting examples of modulesstored in the memory of the computing device include: a first module toreceive measurements from one or more sensors and a second module tocontrol one or more devices of the system 100.

Computing device 402 also includes one media output component 408 forpresenting information to a user 400. Media output component 408 is anycomponent capable of conveying information to user 400. In someembodiments, media output component 408 includes an output adapter suchas a video adapter and/or an audio adapter. An output adapter isoperatively coupled to processor 404 and is further configured to beoperatively coupled to an output device such as a display device (e.g.,a liquid crystal display (LCD), organic light emitting diode (OLED)display, cathode ray tube (CRT), or “electronic ink” display) or anaudio output device (e.g., a speaker or headphones).

In some embodiments, client computing device 402 includes an inputdevice 410 for receiving input from user 400. Input device 410 mayinclude, for example, a keyboard, a pointing device, a mouse, a stylus,a touch sensitive panel (e.g., a touch pad or a touch screen), a camera,a gyroscope, an accelerometer, a position detector, and/or an audioinput device. A single component such as a touch screen may function asboth an output device of media output component 408 and input device410.

Computing device 402 may also include a communication interface 412,which is configured to communicatively couple to a remote device such asserver system 302 or a web server. Communication interface 412 mayinclude, for example, a wired or wireless network adapter or a wirelessdata transceiver for use with a mobile phone network (e.g., GlobalSystem for Mobile communications (GSM), 3G, 4G or Bluetooth) or othermobile data network (e.g., Worldwide Interoperability for MicrowaveAccess (WIMAX)).

Stored in memory 406 are, for example, computer-readable instructionsfor providing a user interface to user 400 via media output component408 and, optionally, receiving and processing input from input device410. A user interface may include, among other possibilities, a webbrowser and an application. Web browsers enable users 400 to display andinteract with media and other information typically embedded on a webpage or a website from a web server. An application allows users 400 tointeract with a server application. The user interface, via one or bothof a web browser and an application, facilitates display of informationrelated to the process of producing a single crystal silicon ingot withlow oxygen content.

In the example embodiment, system 100 produces silicon crystal ingotssuitable for use in device manufacturing. Advantageously, system 100 maybe used to produce silicon crystal 27, a substantial portion or all ofwhich is substantially free of agglomerated intrinsic point defects.Furthermore, system 100 may be used to produce crystal 27 havingsubstantially no agglomerated defects that are larger than approximatelyone hundred twenty nanometers (nm) in diameter, or more particularly,approximately ninety nm in diameter. The shape of the melt-solid ormelt-crystal interface and the pull speed is controlled during crystalgrowth to limit and/or suppress the formation of agglomerated intrinsicpoint defects.

During production, oxygen is introduced into silicon crystal ingotsthrough the melt-solid or melt crystal interface. However, oxygen maycause various defects in wafers produced from the ingots, reducing theyield of semiconductor devices. Accordingly, it is desirable to producesilicon crystal ingots with a low oxygen concentration. Using themethods described herein, silicon crystal ingots are produced having anoxygen concentration less than approximately 5 parts per million atoms(ppma).

Without being limited to any particular theory, oxygen is introducedinto the growing silicon crystal ingot emerging from the melt by aninteracting series of events, each of which is influenced by at leastone process parameter as described herein below. SiO is introduced intothe melt via dissolution at the crucible wall. The SiO introduced at thecrucible wall may be moved elsewhere in the melt via flow induced bybuoyancy forces created by localized heating of the melt neat thecrucible wall. The SiO may be further moved by additional flow inducedby the rotation rate of the crystal at the melt-crystal interface aswell as rotation rate of the crucible itself. The concentration of SiOin the melt may be reduced via evaporation from the melt at the exposedsurface of the melt. The interaction of any combination of dissolution,convection, and evaporation of SiO within the melt influences theconcentration of SiO in the melt situated near the crystal-meltinterface that is formed into the silicon crystal ingot. In variousaspects, any one or more process parameters are simultaneously regulatedto reduce the concentration of SiO situated near the melt-crystalinterface, and consequently reduce the oxygen concentration within thesilicon crystal ingot formed according to the method.

In various embodiments, various process parameters are regulatedsimultaneously to facilitate producing silicon crystal ingots with a lowoxygen concentration. In one embodiment, the various process parametersare regulated in at least two stages that include an intermediate bodygrowth stage corresponding to growth of the silicon crystal ingot up toan intermediate ingot lengths of approximately 800 mm, and a late bodygrowth stage corresponding to growth of the silicon crystal ingot froman intermediate ingot length of approximately 800 mm up to the totalingot length. In this embodiment, the regulation of the various processparameters in at least two different stages accounts for changes in thenature of the interaction of dissolution, convection, evaporation of SiOwithin the melt, depth of the melt in the crucible, and the flow cellswithin the melt in the crucible as the silicon crystal ingot grows inlength.

In particular, the role of convection is modified over the formation ofthe entire silicon crystal ingot due to a decrease in the depth of themelt within the crucible associated with growth of the silicon crystalingot, as described in detail below. As a result, at the late bodygrowth stage, the regulation of at least one process parameter ismodified differently relative to the regulation of these same parametersat the intermediate body growth stage. In some embodiments, at the latebody growth stage, the regulation of at least three process parametersis modified differently relative to the regulation of these sameparameters at the intermediate body growth stage. As described hereinbelow, the regulation of the process parameters modulate various factorsrelated to the convection of SiO within the melt at the late body growthstage. In one embodiment, the process parameters with modifiedregulation during the late body growth stage include, but are notlimited to: seed rotation rate, crucible rotation rate, and magneticfield strength.

Referring again to FIG. 4, seed rotation rate refers to the rate atwhich pull shaft or cable 117 rotates seed crystal 115 about axis 38.Seed rotation rate impacts the flow of SiO from crucible 10 to crystal27 and a rate of SiO evaporation from melt 25. Referring again to FIG.2, the flow of SiO from crucible 10 to crystal 27 is influencedgenerally by interactions between crystal flow cell 18 driven by therotation of crystal 27 at the seed rotation rate within melt 25 andbuoyancy flow cell 17 driven by heating of melt 25 within crucible 10.The impact of seed rotation rate on the flow of SiO from crucible 10 tocrystal 27 differs depending on the stage of growth of crystal 27.

FIG. 5A is a cross-sectional view of simulated flowlines and oxygenconcentrations within melt 25 at an intermediate body growth stage,corresponding to growth of crystal 27 up to an intermediate ingot lengthof approximately 800 mm. At the intermediate body growth stage, depth200 of melt 25 within crucible 10 is sufficiently deep to effectivelydecouple interactions between fluid motion induced by crystal flow cell18 and buoyancy flow cell 17. A high seed rotation rate (i.e. 12 rpm)reduces the boundary layer thickness between melt line 36 and the gasabove melt 25 to increase SiO evaporation. Further, a high seed rotationrate decreases melt flow from crucible 10 to crystal 27 by suppressingbuoyancy flow cell 17 with induced crystal flow cell 18, as illustratedin FIG. 5A. Moreover, a high seed rotation rate creates an outwardradial flow that retards the inward flow (i.e., transport) of SiO fromcrucible 10, reducing the oxygen concentration in crystal 27.

FIG. 5B is a cross-sectional view of simulated flowlines and oxygenconcentrations within melt 25 at a late body growth stage, correspondingto growth of crystal 27 from an intermediate ingot length ofapproximately 800 mm up to the total ingot length. Due to removal ofmelt 25 from crucible 10 associated with formation of crystal 27, depth200 at the late body growth stage is shallower with respect to depth 200at intermediate body growth stage as illustrated in FIG. 5A. At asimilarly high seed rotation rate to that used to perform the simulationillustrated in FIG. 5A (i.e. 12 rpm), crystal flow cell 18 contacts theinner wall of crucible 10, causing convection of SiO formed at the innerwall of crucible 10 into crystal 27 formed at the late body growthstage.

FIG. 5C is a cross-sectional view of simulated flowlines and oxygenconcentrations within melt 25 at a late body growth stage calculated ata lower (e.g., 8 rpm) seed rotation rate. Crystal flow cell 18 inducedby the lower seed rotation rate does not extend to the inner wall ofcrucible 10, but instead is excluded by buoyancy cell 17. As a result,the flow of SiO produced at the inner wall of crucible 10 to crystal 27is disrupted, thereby reducing the oxygen concentration within crystal27 formed at the late body growth stage at reduced seed rotation rate.

As described herein, the transition from an intermediate to a late bodygrowth stage is a soft transition. The transition may vary depending onvarious parameters of the process, such as crucible size, shape, depthof melt, modeling parameters, and the like. Generally, at theintermediate body growth stage, parameters are such that there arelimited or no interactions between fluid motion induced by crystal flowcell 18 and buoyancy flow cell 17; the crystal flow cell 18 and buoyancyflow cell 17 are effectively decoupled. At the late body growth stage,parameters are such that there are interactions between fluid motioninduced by crystal flow cell 18 and buoyancy flow cell 17; the crystalflow cell 18 and buoyancy flow cell 17 are effectively coupled. By wayof non-limiting example, late body growth stage occurs when less thanabout 37% of the initial mass of melt 25 is left in crucible 10 in anembodiment that includes an initial melt mass of 250 kg in a crucible 10with an inner diameter of about 28 inches. In various embodiments, depth200 of melt 25 within crucible 10 is monitored to identify thetransition from the intermediate to a late body growth stage. In otherexamples, the late body growth stage occurs when less than about 35%,less than about 40%, less than about 45%, or less than about 50% of theinitial mass of melt 25 is left in crucible 10. In some embodiments, thetransition from intermediate to late body growth stage is determinedbased on the depth of melt 25, or any other suitable parameter.

In various embodiments, the method includes regulating the seed rotationrate in at least two stages including, but not limited to, theintermediate body growth stage and the late body growth stage. In oneembodiment, the method includes rotating crystal 27 during theintermediate body growth stage at a seed rotation rate ranging fromapproximately 8 to 14 rpm, and more specifically 12 rpm. In thisembodiment, the method further includes reducing the seed rotation rateat the late body growth stage to a seed rotation rate ranging fromapproximately 6 rpm to 8 rpm, and more specifically 8 rpm.

In another embodiment, the seed rotation rate may be reduced accordingto the intermediate ingot length. By way of non-limiting example, theseed rotation rate may be regulated to approximately 12 rpm forintermediate ingot lengths up to approximately 850 mm, and may befurther regulated to linearly decrease to approximately 8 rpm at anintermediate ingot length of approximately 950 mm, and then regulateseed rotation rate at approximately 8 rpm up to the total ingot length,as illustrated in FIG. 9. As also illustrated in FIG. 9, the oxygencontent of the crystal within the body length ranging from approximately800 mm to the total ingot length is reduced compared to a crystal formedat a constant seed rotation rate of approximately 12 rpm. FIG. 6 is agraph comparing the simulated oxygen concentration of crystals formed atseed rotation rates according to three rotation schedules: a) rotationat 12 rpm for the formation of the entire crystal; b) rotation at 12 rpmup to an intermediate crystal length of 900 mm followed by rotation at 8rpm for formation of the remaining crystal length; and c) rotation at 12rpm up to an intermediate crystal length of 900 mm followed by rotationat 6 rpm for formation of the remaining crystal length. As illustratedin FIG. 6, lower seed rotation rates reduced oxygen concentration withinthe portion of the crystal formed at the late body growth stage.

Crucible rotation rate may further influence the oxygen concentrationswithin crystals 27 formed according to embodiments of the method.Crucible rotation rate refers to the rate at which crucible 10 isrotated about axis 38 using crucible drive unit 107. Crucible rotationrate impacts the flow of SiO from crucible 10 to crystal 27 and anamount of SiO evaporating from melt 25. A high crucible rotation ratereduces both a boundary layer thickness between crucible 10 and melt 25,and a boundary layer thickness between melt line 36 and the gas abovemelt 25. However, to minimize the oxygen concentration in crystal 27, athicker boundary layer between crucible 10 and melt 25 is desired toreduce the SiO transport rate, while a thinner boundary layer betweenmelt line 36 and the gas above melt 25 is desired to increase the SiOevaporation rate. Accordingly, the crucible rotation rate is selected tobalance the competing interests of a high boundary layer thicknessbetween crucible 10 and melt 25 resulting from slower crucible rotationrates and a low boundary layer thickness between melt line 36 and thegas above melt 25 resulting from higher crucible rotation rates.

Changes in depth 200 of melt 10 between intermediate body growth stageand late body growth stage described herein above influence the impactof modulation of crucible rotation rate on oxygen concentration in amanner similar to the influence of seed rotation rate described hereinpreviously. In various embodiments, the method includes regulating thecrucible rotation rate in at least two stages including, but not limitedto, the intermediate body growth stage and the late body growth stage.In one embodiment, the method includes rotating crucible 10 at theintermediate body growth stage at a crucible rotation rate ranging fromapproximately 1.3 rpm to approximately 2.2, and more specifically 1.7rpm. In this embodiment, the method further includes reducing thecrucible rotation rate at the late body growth stage to a cruciblerotation rate ranging from approximately 0.5 rpm to approximately 1.0rpm, and more specifically 1 rpm.

FIGS. 7A and 7B are graphs showing a simulated oxygen concentrationwithin silicon ingots as a function of the crucible rotation rate atlate body growth stage. The silicon ingots of FIG. 7A were formed usingan embodiment of the method in which the seed rotation rate was reducedfrom 12 rpm to 6 rpm at late body growth stage, and the cruciblerotation rate was reduced from about 1.7 rpm to 1 rpm or 1.5 rpm at latebody growth stage. The silicon ingots of FIG. 7B were formed using anembodiment of the method in which the seed rotation rate was reducedfrom 12 rpm to 8 rpm at late body growth stage, and the cruciblerotation rate was reduced from about 1.7 rpm to 0.5 rpm, 1 rpm, or 1.5rpm at late body growth stage. In both simulations, lower cruciblerotation rates were associated with lower oxygen concentrations withinthe resulting silicon ingot.

The method may further include regulating magnet strength in at leasttwo stages including, but not limited to, the intermediate body growthstage and the late body growth stage. Magnet strength refers to thestrength of the cusped magnetic field within the vacuum chamber. Morespecifically, magnet strength is characterized by a current throughcoils 31 and 33 that is controlled to regulate magnetic strength.Magnetic strength impacts the flow of SiO from crucible 10 to crystal27. That is, a high magnetic strength minimizes the flow of SiO fromcrucible 10 to crystal 27 by suppressing a buoyancy force within melt25. As the magnetic field suppresses the buoyancy flow, it decreases thedissolution rate of the quartz crucible, thus lowering the interstitialoxygen incorporated into the crystal. However, if the magnetic fieldstrength increases beyond a certain level, further retardation in thebuoyancy flow may result in decreasing the evaporation rate at the meltfree surface, thus raising the interstitial oxygen levels. Due todifferences in the relative contribution of buoyancy flow to the oxygencontent of the crystal at the late body formation stage relative to theintermediate body formation stage as described previously herein, anadjustment to the magnet strength at the late body formation stageenables appropriate modulation of buoyancy flow to reduce oxygen withinthe crystal formed at the late body formation stage.

In various embodiments, the method includes regulating the magneticfield strength in at least two stages including, but not limited to, theintermediate body growth stage and the late body growth stage. In oneembodiment, the method includes regulating the magnetic field strengthat the intermediate body growth stage such that the magnetic fieldstrength is approximately 0.02 to 0.05 Tesla (T) at an edge of crystal27 at the melt-solid interface and approximately 0.05 to 0.12 T at thewall of crucible 10. In another aspect, the method includes regulatingthe magnetic field strength at the late body growth stage such that themagnetic field strength is approximately 150% of the magnetic fieldstrength used during the intermediate body growth stage, correspondingto approximately 0.03 to 0.075 T at an edge of crystal 27 at themelt-solid interface and approximately 0.075 to 0.18 T at the wall ofcrucible 10.

FIGS. 8A, 8B, and 8C are cross-sectional views of simulated flowlinesand total speeds within melt 25 at a late body growth stage. FIG. 8A wassimulated using magnetic field strengths corresponding to 50% of themagnetic field used at intermediate body growth stage (i.e.,approximately 0.01 to 0.025 T at an edge of crystal 27 at the melt-solidinterface and approximately 0.025 to 0.06 T at the wall of crucible 10).FIG. 8B was simulated using magnetic field strengths corresponding to95% of the magnetic field used at intermediate body growth stage (i.e.,approximately 0.019 to 0.0475 T at an edge of crystal 27 at themelt-solid interface and approximately 0.0475 to 0.114 T at the wall ofcrucible 10). FIG. 8C was simulated using magnetic field strengthscorresponding to 150% of the magnetic field used at intermediate bodygrowth stage (i.e., approximately 0.03 to 0.075 T at an edge of crystal27 at the melt-solid interface and approximately 0.075 to 0.18 T at thewall of crucible 10). Comparing FIGS. 8A, 8B, and 8C, as the strength ofthe magnetic field increases, flow 300 from the bottom of crucible 10 tomelt-crystal interface 302 transitions from relatively high convectionto melt-crystal interface 302 at low magnetic field strength (FIG. 8A)to a relatively little convection at higher magnetic field strengths.This suppression of buoyancy flow within melt 25 by the increasedmagnetic field results in lower oxygen concentration in the resultingsilicon ingot, as summarized in Table 1 below. At 150% magnetic fieldstrength, the simulated oxygen concentration was within the desiredrange below 5% parts per million atoms (ppma).

TABLE 1 Effect of Magnetic Field Strength at Late Body Growth Stage onOxygen Concentration in Silicon Ingots Magnetic Field Strength SimulatedOxygen (% intermediate body Concentration growth stage field strength)(ppma) 50% 9.3 95% 6.4 150%  4.5

One or more additional process parameters may be regulated to facilitateproducing silicon crystal ingots with a low oxygen concentration.However, the effects of these additional process parameters are notsensitive to the changes in the depth 200 of melt 25 within crucible 10during growth of crystal 27. Consequently, the regulation of theadditional process parameters described herein remains essentially thesame between different stages of crystal growth, as described inadditional detail below.

One additional process parameter that is controlled, at least in someembodiments, is wall temperature of crucible 10. The wall temperature ofcrucible 10 corresponds to a dissolution rate of crucible 10.Specifically, the higher the wall temperature of crucible 10, the fasterthat portions of crucible 10 will react with and dissolve into melt 25,generating SiO into the melt and potentially increasing an oxygenconcentration of crystal 27 via the melt-crystal interface. Accordingly,reducing the wall temperature of crucible 10, as used herein, equates toreducing the dissolution rate of crucible 10. By reducing the walltemperature of crucible 10 (i.e., reducing the dissolution rate ofcrucible 10), the oxygen concentration of crystal 27 can be reduced.Wall temperature may be regulated by controlling one or more additionalprocess parameters including, but not limited to heater power and meltto reflector gap.

Heater power is another process parameter that may be controlled in someembodiments to regulate the wall temperature of crucible 10. Heaterpower refers to the power of side and bottom heaters 105 and 106.Specifically, relative to typical heating configurations, by increasinga power of side heater 105 and reducing a power of bottom heater 106, ahot spot on the wall of crucible 10 is raised close to the melt line 36.As the wall temperature of crucible 10 at or below melt line 36 islower, the amount of SiO generated by melt 25 reacting with crucible 10is also lower. The heater power configuration also impacts melt flow byreducing the flow (i.e., transport) of SiO from crucible 10 to singlecrystal 27. In this embodiment, a power of bottom heater 106 isapproximately 0 to 5 kilowatts, and more specifically approximately 0kilowatts, and a power of side heater 105 is in a range fromapproximately 100 to 125 kilowatts. Variations in the power of sideheater 105 may be due to, for example, variation in a hot zone age frompuller to puller.

In some embodiments, melt to reflector gap is an additional processparameter that is controlled to regulate the wall temperature ofcrucible 10. Melt to reflector gap refers to a gap between melt line 36and a heat reflector (not shown). Melt to reflector gap impacts the walltemperature of crucible 10. Specifically, a larger melt to reflector gapreduces the wall temperature of crucible 10. In this embodiment, themelt to reflector gap is between approximately 60 mm and 80 mm, and morespecifically 70 mm.

Seed lift is an additional process parameter that is controlled toregulate the flow of SiO from crucible 10 to crystal 27. Seed liftrefers to the rate at which pull shaft or cable 117 lifts seed crystal115 out of melt 25. In one embodiment, seed crystal 115 is lifted at arate in a range of approximately 0.42 to 0.55 millimeters per minute(mm/min), and more specifically 0.46 mm/min for 300 mm product. Thispull rate is slower than pull rates typically used for smaller diameter(e.g., 200 mm) crystals. For example, the seed lift for 200 mm productmay be in a range of approximately 0.55 to 0.85 mm/min, and morespecifically 0.7 mm/min.

Pull speed is an additional process parameter that may be regulated tocontrol the defect quality of the crystal. For example, using SP2 laserlight scattering, the detected agglomerated point defects generated bythe process described herein may be less than 400 counts for defectsless than 60 nm, less than 100 counts for defects between 60 and 90 nm,and less than 100 counts for less defects between 90 and 120 nm.

In some embodiments, inert gas flow is an additional process parameterthat is controlled to regulate the SiO evaporation from melt 25. Inertgas flow, as described herein, refers to the rate at which argon gasflows through vacuum chamber 101. Increasing the argon gas flow ratesweeps more SiO gas above melt line 36 away from crystal 27, minimizinga SiO gas partial pressure, and in turn increasing SiO evaporation. Inthis embodiment, the argon gas flow rate is in a range fromapproximately 100 slpm to 150 slpm.

Inert gas pressure is an additional process parameter also controlled toregulate the SiO evaporation from melt 27 in some embodiments. Inert gaspressure, as described herein, refers to the pressure of the argon gasflowing through vacuum chamber 101. Decreasing the argon gas pressureincreases SiO evaporation and hence decreases SiO concentration in melt25. In this embodiment, the argon gas pressure ranges from approximately10 torr to 30 torr.

In suitable embodiments, cusp position is an additional processparameter that is controlled to regulate the wall temperature ofcrucible 10 and the flow of SiO from crucible 10 to crystal 27. Cuspposition, as described herein, refers to the position of the cusp of themagnetic field generated by coils 31 and 33. Maintaining the cuspposition below melt line 36 facilitates reducing the oxygenconcentration. In this embodiment, the cusp position is set in a rangefrom approximately 10 mm to 40 mm below melt line 36, more specifically,in a range of approximately 25 mm to 35 mm below melt line 36, and evenmore specifically, at approximately 30 mm.

By controlling process parameters (i.e., heater power, crucible rotationrate, magnet strength, seed lift, melt to reflector gap, inert gas flow,inert gas pressure, seed rotation rate, and cusp position) as describedabove, a plurality of process parameters (i.e., a wall temperature of acrucible, a flow of SiO from the crucible to a single crystal, and anevaporation of SiO from a melt) are regulated to produce silicon ingotshaving a low oxygen concentration. In one embodiment, the methodsdescribed herein facilitate producing a silicon ingot with an ingotdiameter greater than approximately 150 millimeters (mm), a total ingotlength of at least approximately 900 mm, and an oxygen concentrationless than 5 ppma. In another embodiment, the methods described hereinfacilitate producing a silicon ingot with an ingot diameter ranging fromapproximately 150 mm to 460 mm, specifically approximately 300 mm, andan oxygen concentration less than 5 ppma. In another additionalembodiment, the methods described herein facilitate producing a siliconingot with a total ingot length ranging from approximately 900 mm to1200 mm, and an oxygen concentration less than 5 ppma.

Wafers having low oxygen concentration using the systems and methodsdescribed herein may be advantageous in a variety of applications. Forexample, insulated-gate bipolar transistors (IGBTs), high qualityradio-frequency (RF), high resistivity silicon on insulator (HR-SOI),and charge trap layer SOI (CTL-SOI) applications may benefit from thelow oxygen concentration because they achieve high resistivity and donot have p-n junctions. Wafers produced for IGBT applications using themethods described herein may, for example, have 30 to 300 ohm-centimeter(ohm-cm) N-type resistivity or greater than 750 ohm-cm N/P-typeresistivity. Further, wafers produced for RF, HR-SOI, and/or CTL-SOIapplicants using the methods described herein may have, for example,greater than 750 ohm-cm P-type wafers. Wafers produced by the describedsystems and methods may also be used as handle wafers.

For P-type wafers produced using the methods described herein, boron,aluminum, germanium, and/or indium may be suitably used has a majoritycarrier, and red phosphorus, phosphorus, arsenic, and/or antimony may beused as a minority carrier. For N-type wafers produced using the methodsdescribed herein, red phosphorus, phosphorus, arsenic, and/or antimonymay be used as the majority carrier, and boron, aluminum, germanium,and/or indium may be used as the minority carrier.

To improve mechanical strength and slip performance, wafers producedusing the methods described herein may be co-doped (e.g., by doping thesingle crystal that forms the ingot) with nitrogen or carbon, due to therelatively low Oi of the wafers. For example, the nitrogen concentrationmay be varied between 0 to 8e15 atoms per cubic centimeter, and thecarbon concentration may be varied between 0.0 to 2.0 ppma.

Example systems and methods of producing single crystal silicon ingotswith relatively low oxygen concentration from a melt formed frompolycrystalline silicon are described herein. These methods takeadvantage of changes in the structure of flow cells in the melt betweena first and second stage of production of the ingot to producerelatively low oxygen silicon. During the first stage, the silicon ingotis relatively small and the depth of the melt is relatively deep. Thesecond stage is characterized by a depleted melt depth within thecrucible due to formation of the silicon ingot. In this second stage, aflow cell induced by rotation of the silicon ingot within the melt maycontact the bottom of the crucible, causing unwanted inclusion ofsilicon oxide formed at the crucible bottom into the growing crystalingot. The methods and systems described herein control production ofthe ingot to limit the including of the unwanted silicon oxide.Generally, at least one process parameter is changed during the secondstage relative to its value during the first stage. Non-limitingexamples of changes in process parameters from the first stage to thesecond stage include: reduced crystal rotation rate, reduced cruciblerotation rate, increased magnetic field strength, and any combinationthereof. For example, in some embodiments, the silicon ingot is rotatedmore slowly during the second stage to reduce contact of the rotationinduced flow cell with the bottom of the crucible, and thereby reducethe amount oxygen included in the silicon ingot.

The systems and methods described herein enable the formation of singlecrystal silicon ingots with low oxygen concentration maintained over alonger ingot length than was achieved using previous methods. A detaileddescription of the effects of these changes in process parameters on thestructure of flow cells within the crucible and the oxygen content ofthe silicon ingots formed using the method on various embodiments, aredescribed in further detail herein.

Embodiments of the methods described herein achieve superior resultscompared to prior methods and systems. For example, the methodsdescribed herein facilitate producing silicon ingots with a lower oxygenconcentration than at least some known methods. Further, unlike at leastsome known methods, the methods described herein may be used for theproduction of ingots having a diameter greater than 150 mm.

When introducing elements of the present invention or the embodiment(s)thereof, the articles “a”, “an”, “the” and “said” are intended to meanthat there are one or more of the elements. The terms “comprising”,“including” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.

Approximating language, as used herein throughout the specification andclaims, may be applied to modify any quantitative representation thatcould permissibly vary without resulting in a change in the basicfunction to which it is related. Accordingly, a value modified by a termor terms, such as “about,” “approximately,” and “substantially,” is notto be limited to the precise value specified. In at least someinstances, the approximating language may correspond to the precision ofan instrument for measuring the value. Here and throughout thespecification and claims, range limitations may be combined and/orinterchanged; such ranges are identified and include all the sub-rangescontained therein unless context or language indicates otherwise.

As various changes could be made in the above without departing from thescope of the invention, it is intended that all matter contained in theabove description and shown in the accompanying drawings shall beinterpreted as illustrative and not in a limiting sense.

1. A method for producing a silicon ingot, the method comprising:withdrawing a seed crystal from a melt comprising an amount of meltedsilicon in a crucible to form the silicon ingot, the crucible enclosedin a vacuum chamber containing a cusped magnetic field; and regulatingat least one process parameter, wherein the at least one processparameter is regulated in at least two stages, the at least two stagescomprising: a first stage corresponding to formation of the siliconingot up to an intermediate ingot length; and a second stagecorresponding to formation of the silicon ingot from the intermediateingot length to the total ingot length; wherein regulating the at leastone process parameter during the second stage comprises at least one of:reducing a crystal rotation rate relative to the crystal rotation rateduring the first stage; reducing a crucible rotation rate relative tothe crucible rotation rate during the first stage; and increasing amagnetic field strength relative to the magnetic field strength duringthe first stage.
 2. The method of claim 1, wherein regulating the atleast one process parameter comprises regulating the crystal rotationrate ranges between 8 rpm to 14 rpm during the first stage andregulating the crystal rotation rate ranges between 6 rpm to 8 rpmduring the second stage.
 3. The method of claim 1, wherein: regulatingthe at least one process parameter comprises regulating the crystalrotation rate to 12 rpm during the first stage; and regulating the atleast one process parameter during the second stage comprises:decreasing the crystal rotation rate over time from 12 rpm at the end ofthe first stage to 8 rpm when the silicon ingot length reaches 950 mm;and maintaining the crystal rotation rate at 8 rpm during formation ofthe silicon ingot between the intermediate ingot length of 950 mm andthe total ingot length.
 4. The method of claim 1, wherein regulating theat least one process parameter comprises regulating the cruciblerotation rate between 1.3 rpm and 2.2 rpm during the first stage, andbetween 0.5 rpm and 1.7 rpm during the second stage.
 5. The method ofclaim 1, wherein regulating at least one process parameter comprisesregulating the crucible rotation rate to 1.7 rpm during the first stage,and between 0.5 rpm and 1.7 rpm during the second stage.
 6. The methodof claim 1, wherein: regulating the at least one process parametercomprises regulating the crucible rotation rate to 1.7 rpm during thefirst stage; and regulating the at least one process parameter duringthe second stage comprises: decreasing the crucible rotation rate overtime from 1.7 rpm at the end of the first stage to 0.5 rpm when thesilicon ingot length reaches 950 mm; and maintaining the crystalrotation rate at 0.5 rpm during formation of the silicon ingot betweenthe intermediate ingot length of 950 mm and the total ingot length. 7.The method of claim 1, wherein regulating the at least one processparameter during the second stage comprises regulating the magneticfield strength during the second stage to 150% of the magnetic fieldstrength during the first stage.
 8. The method of claim 1, wherein:regulating the at least one process parameter comprises regulating,during the first stage, the magnetic field strength to a strengthbetween 0.02 and 0.05 Tesla at an edge of the silicon ingot at amelt-solid interface, and regulating the magnetic field strength to astrength between 0.05 and 0.12 Tesla at a wall of the crucible; andregulating the at least one process parameter during the second stagecomprises regulating the magnetic field strength to a strength between0.03 and 0.075 Tesla at the edge of the silicon ingot at the melt-solidinterface, and regulating the magnetic field strength to a strengthbetween 0.075 and 0.18 Tesla at the wall of the crucible.
 9. The methodof claim 1, further comprising controlling a plurality of additionalprocess parameters during the first and second stages, the plurality ofadditional process parameters comprising at least one of a heater power,a melt to reflector gap, a seed lift, a pull speed, an inert gas flow,an inert gas pressure, and a cusp position, wherein controlling theplurality of additional process parameters during the first and secondstages comprises, for each parameter of the plurality of additionalprocess parameters, controlling the parameter to be substantially thesame during the first and second stages. 10-26. (canceled)
 27. A crystalgrowing system for producing a silicon ingot, the system comprising avacuum chamber; a crucible disposed within the vacuum chamber, thecrucible rotatable about an axis of symmetry, and configured to hold amelt including molten silicon; a pull shaft movable along the axis ofsymmetry and rotatable about the axis of symmetry, and configured tohold a seed crystal; at least one magnet to generate a controllablecusped magnetic field within the crucible; a control unit comprising aprocessor and a memory, the memory storing instruction that, whenexecuted by the processor, cause the processor to: withdraw the seedcrystal from a melt in the crucible to form the silicon ingot; andregulate at least one process parameter, wherein the at least oneprocess parameter is regulated in at least two stages, the at least twostages comprising: a first stage corresponding to formation of thesilicon ingot up to an intermediate ingot length; and a second stagecorresponding to formation of the silicon ingot from the intermediateingot length to the total ingot length; wherein the instruction, whenexecuted by the processor, cause the processor to regulate the at leastone process parameter by at least one of: reducing a crystal rotationrate relative to the crystal rotation rate during the first stage;reducing a crucible rotation rate relative to the crucible rotation rateduring the first stage; and increasing a magnetic field strengthproduced by the at least one magnet relative to the magnetic fieldstrength produced by the at least one magnet during the first stage. 28.The system of claim 27, wherein the memory stores instruction that, whenexecuted by the processor, cause the processor to regulate the at leastone process parameter by regulating the crystal rotation rate rangesbetween 8 rpm to 14 rpm during the first stage and regulating thecrystal rotation rate ranges between 6 rpm to 8 rpm during the secondstage.
 29. The system of claim 27, wherein the memory stores instructionthat, when executed by the processor, cause the processor to regulatethe at least one process parameter by: regulating the crystal rotationrate to 12 rpm during the first stage; and decreasing the crystalrotation rate over time from 12 rpm at the end of the first stage to 8rpm when the silicon ingot length reaches 950 mm; and maintaining thecrystal rotation rate at 8 rpm during formation of the silicon ingotbetween the intermediate ingot length of 950 mm and the total ingotlength.
 30. The system of claim 27, wherein the memory storesinstruction that, when executed by the processor, cause the processor toregulate the at least one process parameter by regulating the cruciblerotation rate between 1.3 rpm and 2.2 rpm during the first stage, andbetween 0.5 rpm and 1.7 rpm during the second stage.
 31. The system ofclaim 27, wherein the memory stores instruction that, when executed bythe processor, cause the processor to regulate the at least one processparameter by regulating the crucible rotation rate to 1.7 rpm during thefirst stage, and between 0.5 rpm and 1.7 rpm during the second stage.32. The system of claim 27, wherein the memory stores instruction that,when executed by the processor, cause the processor to regulate the atleast one process parameter by: regulating the crucible rotation rate to1.7 rpm during the first stage; and decreasing the crucible rotationrate over time from 1.7 rpm at the end of the first stage to 0.5 rpmwhen the silicon ingot length reaches 950 mm; and maintaining thecrystal rotation rate at 0.5 rpm during formation of the silicon ingotbetween the intermediate ingot length of 950 mm and the total ingotlength.
 33. The system of claim 27, wherein the memory storesinstruction that, when executed by the processor, cause the processor toregulate the at least one process parameter by regulating the magneticfield strength during the second stage to 150% of the magnetic fieldstrength during the first stage.
 34. The system of claim 27, wherein thememory stores instruction that, when executed by the processor, causethe processor to regulate the at least one process parameter by:regulating, during the first stage, the magnetic field strength to astrength between 0.02 and 0.05 Tesla at an edge of the silicon ingot ata melt-solid interface, and to a strength between 0.05 and 0.12 Tesla ata wall of the crucible; and regulating, during the second stage, themagnetic field strength to a strength between 0.03 and 0.075 Tesla atthe edge of the silicon ingot at the melt-solid interface, and to astrength between 0.075 and 0.18 Tesla at the wall of the crucible. 35.The system of claim 27, further wherein the memory stores furtherinstruction that, when executed by the processor, cause the processor tocontrol a plurality of additional process parameters during the firstand second stages.
 36. The system of claim 35, wherein the plurality ofadditional process parameters comprise at least one of a heater power, amelt to reflector gap, a seed lift, a pull speed, an inert gas flow, aninert gas pressure, and a cusp position.
 37. The system of claim 36,wherein the memory stores instruction that, when executed by theprocessor, cause the processor, for each parameter of the plurality ofadditional process parameters, to control the process parameter to besubstantially the same during the first and second stages.